Finite Group Databasebeta

← C2×#22572660 #31734374

Subgroups — C2×#22572660 #31734374

Order 17152.

1878 conjugacy classes of subgroups.

The subgroup lattice has 720 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16864101C211yesmaximal, characteristic
2C2×#16864081C211yesmaximal, characteristic
3#22572660C2116yesmaximal, direct product factor
4C2×#16863803C211yesmaximal, characteristic, complemented
5C2×#16863731C211yesmaximal, characteristic, complemented
6C2×#16863740C211yesmaximal, characteristic, complemented
7C2×#16863728C211yesmaximal, characteristic, complemented
8C2×#16863726C211yesmaximal, characteristic, complemented
9C2×#16863706C211yesmaximal, characteristic, complemented
10C2×#16863680C211yesmaximal, characteristic, complemented
11C2×#16863655C211yesmaximal, characteristic, complemented
12C2×#16863637C211yesmaximal, characteristic, complemented
13C2×#16863502C211yesmaximal, characteristic, complemented
14C2×#16863467C211yesmaximal, characteristic
15C2×#16863435C211yesmaximal, characteristic, complemented
16C22×#106×C67C211yesmaximal, characteristic, complemented
17C22×Dic268C2211yescharacteristic
18C22×#11761611C2211yescharacteristic
19#16864101—24no—
20#16864101C2218yes—
21#16864081—24no—
22#16864081C2218yes—
23C2×#14524042C2211yescharacteristic
24C2×#14524038—21no—
25C2×#14524034C2211yescharacteristic
26C2×#14524033—21no—
27C2×#14524033—21no—
28C2×#14524026—21no—
29C2×#14524023C2211yescharacteristic
30C2×#14524023C2211yescharacteristic
31C2×#14524022—21no—
32C2×#14524022C2211yescharacteristic
33C2×#14524022C2211yescharacteristic
34C2×#14524021—21no—
35C2×#14524008C2211yescharacteristic
36C2×#14524008C2211yescharacteristic
37C2×C4×C22⋊D67—21no—
38C2×C4×C22⋊D67C2211yescharacteristic
39C2×#14524002—21no—
40C2×#14524001C2211yescharacteristic
41C2×C4⋊C4×D67C2211yescharacteristic
42#16863803C2218yescomplemented
43#16863740C2218yescomplemented
44#16863731C2218yescomplemented
45#16863728C2218yescomplemented
46#16863726C2218yescomplemented
47#16863706C2218yescomplemented
48#16863680C2218yescomplemented
49#16863655C2218yescomplemented
50#16863637C2218yescomplemented
51#16863502C2218yescomplemented
52#16863467C2218yes—
53#16863435C2218yescomplemented
54C2×#14523977C2211yescharacteristic
55C2×#14523976C2211yescharacteristic
56C2×#14523976C2211yescharacteristic
57C2×#14523974C2211yescharacteristic
58C2×#14523974C2211yescharacteristic
59C2×Dic67⋊C8C2211yescharacteristic
60C2×#14523968C2211yescharacteristic
61C2×#14523968C2211yescharacteristic
62C2×#14523966C2211yescharacteristic
63C2×#14523966C2211yescharacteristic
64C2×#14523966C2211yescharacteristic
65C2×#14523966C2211yescharacteristic
66C2×C22⋊(C67⋊C8)C2211yescharacteristic
67C2×(C2×D67)⋊C8C2211yescharacteristic
68C2×#14523953C2211yescharacteristic
69C23×C8×C67C2211yescharacteristic
70C22×C4⋊C4×C67C2211yescharacteristic
71C22×C4⋊C4×C67C2211yescharacteristic
72C2×#106×C67C2211yescharacteristic
73C2×#106×C67C2211yescharacteristic
74C2×#106×C67C2211yescharacteristic
75C2×#106×C67C2211yescharacteristic
76C2×#106×C67C2218yescomplemented
77C22×Dic134—21no—
78C22×Dic134C2311yescharacteristic
79C22×Dic134C2311yescharacteristic
80C22×C22⋊D67D411yescharacteristic
81C22×C4×D67—21no—
82C22×C4×D67C2311yescharacteristic
83C2×Dic268—24no—
84C2×Dic268C2314yes—
85C2×#11761611—24no—
86C2×#11761611C2314yes—
87C22×C67⋊C8C2311yescharacteristic
88C22×C67⋊C8C2311yescharacteristic
89#14524042—22no—
90#14524042C2314yes—
91#14524038—28no—
92#14524034—22no—
93#14524034C2314yes—
94#14524033—28no—
95#14524033—28no—
96#14524026—28no—
97#14524023—22no—
98#14524023—22no—
99#14524023C2314yes—
100#14524023C2314yes—
101#14524022—28no—
102#14524022—22no—
103#14524022—22no—
104#14524022C2314yes—
105#14524022C2314yes—
106#14524021—28no—
107#14524008—22no—
108#14524008—22no—
109#14524008C2314yes—
110#14524008C2314yes—
111C4×C22⋊D67—28no—
112C4×C22⋊D67D414yes—
113C4×C22⋊D67C2314yes—
114#14524002—28no—
115#14524001—22no—
116#14524001C2314yes—
117C2×C4⋊Dic67—21no—
118C2×C4⋊Dic67—21no—
119C2×C4⋊Dic67—21no—
120C2×C4⋊Dic67C2311yescharacteristic
121C2×C4⋊Dic67C2311yescharacteristic
122C2×Dic67⋊C4—21no—
123C2×Dic67⋊C4—21no—
124C2×Dic67⋊C4—21no—
125C2×Dic67⋊C4—21no—
126C2×Dic67⋊C4—21no—
127C2×Dic67⋊C4—21no—
128C2×Dic67⋊C4—21no—
129C2×Dic67⋊C4D411yescharacteristic
130C4⋊C4×D67—22no—
131C4⋊C4×D67C2314yes—
132C2×C22⋊Dic67—21no—
133C2×C22⋊Dic67—21no—
134C2×C22⋊Dic67D411yescharacteristic
135C2×(C2×D67)⋊C4—21no—
136C2×(C2×D67)⋊C4—21no—
137C2×(C2×D67)⋊C4—21no—
138C2×(C2×D67)⋊C4D411yescharacteristic
139C2×C4×Dic67—21no—
140C2×C4×Dic67—21no—
141C2×C4×Dic67—21no—
142C2×C4×Dic67C2311yescharacteristic
143#14523977C2314yes—
144#14523976C2314yes—
145#14523976C2314yes—
146#14523974C2314yes—
147#14523974C2314yes—
148Dic67⋊C8C2314yes—
149#14523968C2314yes—
150#14523968C2314yes—
151#14523966C2314yes—
152#14523966C2314yes—
153#14523966C2314yes—
154#14523966C2314yes—
155C22⋊(C67⋊C8)C2314yes—
156(C2×D67)⋊C8C2314yes—
157#14523953C2314yes—
158C23×C4×C67—21no—
159C23×C4×C67—21no—
160C23×C4×C67C2311yescharacteristic
161C22×C8×C67—24no—
162C22×C8×C67C2311yescharacteristic
163C22×C8×C67C2314yes—
164C22×C8×C67C2311yescharacteristic
165C2×C4⋊C4×C67—22no—
166C2×C4⋊C4×C67—22no—
167C2×C4⋊C4×C67—21no—
168C2×C4⋊C4×C67—21no—
169C2×C4⋊C4×C67C2314yes—
170C2×C4⋊C4×C67C2311yescharacteristic
171C2×C4⋊C4×C67C2314yes—
172C2×C4⋊C4×C67C2311yescharacteristic
173C2×C4⋊C4×C67C2311yescharacteristic
174C2×C4⋊C4×C67C2311yescharacteristic
175#106×C67C2314yes—
176#106×C67C2314yes—
177#106×C67C2314yes—
178#106×C67C2314yes—
179C23×D67C2×D411yescharacteristic
180C2×Dic134—22no—
181C2×Dic134—22no—
182C2×Dic134—22no—
183C2×Dic134—22no—
184C2×Dic134—21no—
185C2×Dic134—21no—
186C2×Dic134—24no—
187C2×Dic134—82no—
188C2×Dic134C2412yes—
189C2×Dic134C2412yes—
190C2×C22⋊D67—24no—
191C2×C22⋊D67C2×D414yes—
192C22×Dic67—21no—
193C22×Dic67—21no—
194C22×Dic67—21no—
195C22×Dic67—21no—
196C22×Dic67C2×D411yescharacteristic
197C22×Dic67C2×D411yescharacteristic
198C22×Dic67C2×D411yescharacteristic
199C2×C4×D67—22no—
200C2×C4×D67—22no—
201C2×C4×D67—24no—
202C2×C4×D67—82no—
203C2×C4×D67C2×D412yes—
204C2×C4×D67C2412yes—
205Dic268—28no—
206#11761611—28no—
207C2×C67⋊C8—22no—
208C2×C67⋊C8—22no—
209C2×C67⋊C8C2412yes—
210C2×C67⋊C8C2412yes—
211C4⋊Dic67—21no—
212C4⋊Dic67—21no—
213C4⋊Dic67—24no—
214C4⋊Dic67—24no—
215C4⋊Dic67—24no—
216C4⋊Dic67C2412yes—
217C4⋊Dic67C2412yes—
218Dic67⋊C4—24no—
219Dic67⋊C4—24no—
220Dic67⋊C4—24no—
221Dic67⋊C4—24no—
222Dic67⋊C4—24no—
223Dic67⋊C4—24no—
224Dic67⋊C4—24no—
225Dic67⋊C4C2×D414yes—
226C22⋊Dic67—24no—
227C22⋊Dic67—24no—
228C22⋊Dic67C2×D414yes—
229(C2×D67)⋊C4—24no—
230(C2×D67)⋊C4—24no—
231(C2×D67)⋊C4—24no—
232(C2×D67)⋊C4C2×D414yes—
233C4×Dic67—24no—
234C4×Dic67—24no—
235C4×Dic67—24no—
236C4×Dic67C2×D412yes—
237C4×Dic67C2412yes—
238C24×C67C2×D411yescharacteristic
239C22×C4×C67—22no—
240C22×C4×C67—22no—
241C22×C4×C67—21no—
242C22×C4×C67—21no—
243C22×C4×C67—21no—
244C22×C4×C67—21no—
245C22×C4×C67—24no—
246C22×C4×C67—24no—
247C22×C4×C67—44no—
248C22×C4×C67—82no—
249C22×C4×C67C2×D411yescharacteristic
250C22×C4×C67C2×D412yes—
251C22×C4×C67C2412yes—
252C22×C4×C67C2411yescharacteristic
253C2×C8×C67—22no—
254C2×C8×C67—28no—
255C2×C8×C67#4114yes—
256C2×C8×C67C2412yes—
257C2×C8×C67C2412yes—
258C4⋊C4×C67—21no—
259C4⋊C4×C67—21no—
260C4⋊C4×C67—24no—
261C4⋊C4×C67—21no—
262C4⋊C4×C67—21no—
263C4⋊C4×C67—24no—
264C4⋊C4×C67C2412yes—
265C4⋊C4×C67C2412yes—
266C4⋊C4×C67C2412yes—
267C4⋊C4×C67C2412yes—
268C23×C67—22no—
269C23×C67—22no—
270C23×C67#13714yes—
271C23×C67C22×D412yes—
272C23×C67C22×D411yescharacteristic
273C22×D67—22no—
274C22×D67—22no—
275C22×D67—22no—
276C22×D67C22×D412yes—
277C2×C4×C67—22no—
278C2×C4×C67—24no—
279C2×C4×C67—22no—
280C2×C4×C67—22no—
281C2×C4×C67—22no—
282C2×C4×C67—22no—
283C2×C4×C67—22no—
284C2×C4×C67—22no—
285C2×C4×C67—48no—
286C2×C4×C67—42no—
287C2×C4×C67—42no—
288C2×C4×C67—42no—
289C2×C4×C67—42no—
290C2×C4×C67—84no—
291C2×C4×C67C22×D412yes—
292C2×C4×C67C22×D411yescharacteristic
293C2×C4×C67C2×#4112yes—
294C2×C4×C672−1+412yes—
295C2×C4×C67C2511yescharacteristic
296C22⋊D67—28no—
297C2×Dic67—22no—
298C2×Dic67—22no—
299C2×Dic67—22no—
300C2×Dic67—22no—
301C2×Dic67—22no—
302C2×Dic67—22no—
303C2×Dic67—22no—
304C2×Dic67—42no—
305C2×Dic67—42no—
306C2×Dic67—42no—
307C2×Dic67—42no—
308C2×Dic67C22×D412yes—
309C2×Dic67C22×D412yes—
310C2×Dic67C22×D412yes—
311C4×D67—24no—
312C4×D67—22no—
313C4×D67—22no—
314C4×D67—84no—
315Dic134—22no—
316Dic134—22no—
317Dic134—22no—
318Dic134—22no—
319Dic134—42no—
320Dic134—42no—
321Dic134—84no—
322C8×C67—22no—
323C8×C67C2×#4114yes—
324C67⋊C8—22no—
325C67⋊C8—22no—
326C22×C67—28no—
327C22×C67—22no—
328C22×C67—22no—
329C22×C67#54712yes—
330C22×C67C2×#13714yes—
331C22×C67C2×#13712yes—
332C22×C67#57712yes—
333C22×C67C23×D411yescharacteristic
334C2×D67—22no—
335C2×D67—22no—
336C2×D67—22no—
337C2×D67—44no—
338C4×C67—22no—
339C4×C67—42no—
340C4×C67—42no—
341C4×C67—42no—
342C4×C67—42no—
343C4×C67#54712yes—
344C4×C67C22×#4111yescharacteristic
345C4×C67C2×2−1+411yescharacteristic
346Dic67—22no—
347Dic67—22no—
348Dic67—22no—
349Dic67—42no—
350Dic67—42no—
351Dic67—42no—
352Dic67—42no—
353C2×#3344—671nomaximal, Sylow
354C2×C67—24no—
355C2×C67#334414yescomplemented
356C2×C67C2×#54711yescharacteristic
357C2×C67C22×#13711yescharacteristic
358C2×C67C2×#57711yescharacteristic
359D67—42no—
360C2×#554—671no—
361C2×#552—671no—
362#3344—6716no—
363C2×#501—671no—
364C2×#484—671no—
365C2×#485—671no—
366C2×#483—671no—
367C2×#483—671no—
368C2×#479—671no—
369C2×#475—671no—
370C2×#470—671no—
371C2×#467—671no—
372C2×#441—671no—
373C2×#435—671no—
374C2×#428—671no—
375C22×#106D6711yescharacteristic, complemented
376C67C2×#334411yescharacteristic, complemented, Sylow
377C22×Q16—671no—
378C22×M16—671no—
379C23×C8C2×D6711yescharacteristic
380#554—678no—
381#554—1344no—
382#552—678no—
383#552—1344no—
384C2×C4⋊Q8—671no—
385C2×#126—1341no—
386C2×#125—671no—
387C2×#125—1341no—
388C2×#125—1341no—
389C2×#123—1341no—
390C2×C22⋊Q8—671no—
391C2×C22⋊Q8—671no—
392C2×C22⋊Q8—671no—
393C2×C22⋊Q8—671no—
394C2×C22⋊Q8—1341no—
395C2×C22⋊Q8—1341no—
396C2×C4×Q8—671no—
397C2×C4×Q8—671no—
398C2×C4×D4—671no—
399C2×C4×D4—1341no—
400C2×#117—671no—
401C2×#117—1341no—
402C22×C4⋊C4—671no—
403C22×C4⋊C4C2×D6711yescharacteristic
404C22×C4⋊C4C2×D6711yescharacteristic
405#501—678no—
406#485—678no—
407#484—678no—
408#483—678no—
409#483—678no—
410#479—678no—
411#475—678no—
412#470—678no—
413#467—678no—
414#441—678no—
415#435—678no—
416#428—678no—
417C2×#107—671no—
418C2×#107—671no—
419C2×#107—671no—
420C2×#106—671no—
421C2×#106—671no—
422C2×#106C2×D6711yescharacteristic
423C2×#106C2×D6711yescharacteristic
424C2×#106C2×D6711yescharacteristic
425C2×#106C2×D6711yescharacteristic
426C2×#106C2×D6718yescomplemented
427C2×C4⋊C8—671no—
428C2×#103—671no—
429C2×#103—671no—
430C2×#103—671no—
431C2×#103—671no—
432C2×#103—671no—
433C2×#103—671no—
434C2×C22⋊C8—671no—
435C2×C22⋊C8—671no—
436C2×#97—671no—
437C22×Q8—671no—
438C22×Q8—671no—
439C22×Q8—1341no—
440C22×D4—671no—
441C23×C4—21no—
442C23×C4—21no—
443C23×C4—671no—
444C23×C4—1341no—
445C23×C4C22×D6711yescharacteristic
446C2×Q16—674no—
447C2×Q16—1344no—
448C2×M16—674no—
449C2×M16—1344no—
450C22×C8—24no—
451C22×C8—671no—
452C22×C8—671no—
453C22×C8C22×D6711yescharacteristic
454C22×C8C22×D6714yes—
455C22×C8C22×D6711yescharacteristic
456C4⋊Q8—674no—
457C4⋊Q8—1342no—
458#126—1348no—
459#125—674no—
460#125—1342no—
461#125—1348no—
462#125—1348no—
463#123—1348no—
464C22⋊Q8—674no—
465C22⋊Q8—674no—
466C22⋊Q8—674no—
467C22⋊Q8—674no—
468C22⋊Q8—1348no—
469C22⋊Q8—1348no—
470C22⋊Q8—1342no—
471C22⋊Q8—1342no—
472C22⋊Q8—1342no—
473C22⋊Q8—1342no—
474C4×Q8—674no—
475C4×Q8—674no—
476C4×Q8—1342no—
477C4×Q8—1342no—
478C4×D4—674no—
479C4×D4—674no—
480C4×D4—1348no—
481#117—674no—
482#117—1348no—
483#117—1342no—
484C2×C4⋊C4—21no—
485C2×C4⋊C4—21no—
486C2×C4⋊C4—22no—
487C2×C4⋊C4—22no—
488C2×C4⋊C4—671no—
489C2×C4⋊C4—671no—
490C2×C4⋊C4—671no—
491C2×C4⋊C4—674no—
492C2×C4⋊C4—1342no—
493C2×C4⋊C4—1341no—
494C2×C4⋊C4—1341no—
495C2×C4⋊C4—1341no—
496C2×C4⋊C4—1341no—
497C2×C4⋊C4—1341no—
498C2×C4⋊C4—1341no—
499C2×C4⋊C4—1341no—
500C2×C4⋊C4—1341no—
501C2×C4⋊C4—1341no—
502C2×C4⋊C4—1341no—
503C2×C4⋊C4C22×D6711yescharacteristic
504C2×C4⋊C4C22×D6711yescharacteristic
505C2×C4⋊C4C22×D6711yescharacteristic
506C2×C4⋊C4C22×D6711yescharacteristic
507C2×C4⋊C4C22×D6714yes—
508C2×C4⋊C4C22×D6714yes—
509C2×C22⋊C4—671no—
510C2×C22⋊C4—671no—
511C2×C22⋊C4—1341no—
512C2×C22⋊C4—1341no—
513C2×C22⋊C4—1341no—
514C2×C22⋊C4—1341no—
515C2×C22⋊C4—1341no—
516C2×C42—671no—
517C2×C42—1341no—
518C2×C42—1341no—
519C2×C42—1341no—
520#107—674no—
521#107—674no—
522#107—674no—
523#106—674no—
524#106—674no—
525#106C22×D6714yes—
526#106C22×D6714yes—
527#106C22×D6714yes—
528#106C22×D6714yes—
529C4⋊C8—674no—
530#103—674no—
531#103—674no—
532#103—674no—
533#103—674no—
534#103—674no—
535#103—674no—
536C22⋊C8—674no—
537C22⋊C8—674no—
538#97—674no—
539C24—671no—
540C24D4×D6711yescharacteristic
541C2×Q8—5362no—
542C2×Q8—672no—
543C2×Q8—672no—
544C2×Q8—1344no—
545C2×Q8—1342no—
546C2×Q8—1342no—
547C2×Q8—1342no—
548C2×Q8—1342no—
549C2×Q8—1341no—
550C2×Q8—1341no—
551C2×D4—674no—
552C2×D4—1344no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—24no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—24no—
561C22×C4—44no—
562C22×C4—82no—
563C22×C4—5362no—
564C22×C4—671no—
565C22×C4—671no—
566C22×C4—671no—
567C22×C4—672no—
568C22×C4—672no—
569C22×C4—1344no—
570C22×C4—1341no—
571C22×C4—1341no—
572C22×C4—1341no—
573C22×C4—1341no—
574C22×C4—1342no—
575C22×C4—1342no—
576C22×C4D4×D6712yes—
577C22×C4D4×D6711yescharacteristic
578C22×C4C23×D6712yes—
579C22×C4C23×D6711yescharacteristic
580Q16—1348no—
581M16—1348no—
582C2×C8—22no—
583C2×C8—28no—
584C2×C8—672no—
585C2×C8—672no—
586C2×C8—1342no—
587C2×C8—1342no—
588C2×C8#1176162814yes—
589C2×C8C23×D6712yes—
590C2×C8C23×D6712yes—
591C4⋊C4—21no—
592C4⋊C4—21no—
593C4⋊C4—24no—
594C4⋊C4—21no—
595C4⋊C4—21no—
596C4⋊C4—24no—
597C4⋊C4—674no—
598C4⋊C4—672no—
599C4⋊C4—672no—
600C4⋊C4—1344no—
601C4⋊C4—1344no—
602C4⋊C4—1344no—
603C4⋊C4—1344no—
604C4⋊C4—1344no—
605C4⋊C4—1344no—
606C4⋊C4—1344no—
607C4⋊C4—1344no—
608C4⋊C4—1341no—
609C4⋊C4—1341no—
610C4⋊C4—1344no—
611C4⋊C4—1344no—
612C4⋊C4C23×D6712yes—
613C4⋊C4C23×D6712yes—
614C4⋊C4C23×D6712yes—
615C4⋊C4C23×D6712yes—
616C22⋊C4—674no—
617C22⋊C4—674no—
618C22⋊C4—1344no—
619C22⋊C4—1344no—
620C22⋊C4—1344no—
621C22⋊C4—1344no—
622C22⋊C4—1344no—
623C42—672no—
624C42—672no—
625C42—1344no—
626C42—1344no—
627C42—1344no—
628C23—22no—
629C23—22no—
630C23—672no—
631C23—1342no—
632C23—1342no—
633C23—1342no—
634C23#1452407214yes—
635C23C2×D4×D6712yes—
636C23C2×D4×D6711yescharacteristic
637Q8—2682no—
638Q8—2682no—
639Q8—5364no—
640Q8—1342no—
641Q8—1342no—
642Q8—1342no—
643Q8—1342no—
644D4—1348no—
645C2×C4—22no—
646C2×C4—24no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—48no—
654C2×C4—42no—
655C2×C4—42no—
656C2×C4—42no—
657C2×C4—42no—
658C2×C4—84no—
659C2×C4—2682no—
660C2×C4—2682no—
661C2×C4—2682no—
662C2×C4—2682no—
663C2×C4—5364no—
664C2×C4—672no—
665C2×C4—672no—
666C2×C4—672no—
667C2×C4—1342no—
668C2×C4—1342no—
669C2×C4—1342no—
670C2×C4—1342no—
671C2×C4—1342no—
672C2×C4—1342no—
673C2×C4—1342no—
674C2×C4—1344no—
675C2×C4—1342no—
676C2×C4—1342no—
677C2×C4C2×D4×D6712yes—
678C2×C4C2×D4×D6711yescharacteristic
679C2×C4C2×#1176162812yes—
680C2×C4#1452409112yes—
681C2×C4C24×D6711yescharacteristic
682C8—22no—
683C8—1342no—
684C8—1342no—
685C8C2×#1176162814yes—
686C22—22no—
687C22—28no—
688C22—22no—
689C22—2684no—
690C22—1342no—
691C22—1342no—
692C22—1342no—
693C22#1686404712yes—
694C22C2×#1452407214yes—
695C22C2×#1452407212yes—
696C22#1686420212yes—
697C22C22×D4×D6711yescharacteristic
698C4—22no—
699C4—42no—
700C4—42no—
701C4—42no—
702C4—42no—
703C4—2682no—
704C4—2682no—
705C4—2682no—
706C4—2682no—
707C4—1342no—
708C4—1342no—
709C4—1342no—
710C4#1686404712yes—
711C4C22×#1176162811yescharacteristic
712C4C2×#1452409111yescharacteristic
713C2—24no—
714C2—2682no—
715C2#2257266014yesdirect product factor
716C2C2×#1686404711yescharacteristic
717C2C22×#1452407211yescharacteristic
718C2C2×#1686420211yescharacteristic
subgroupG/H
centerC23C2×D4×D67
commutator, cosocleC2×C4×C67C25
FrattiniC2×C4C24×D67
FittingC22×#106×C67C2
socleC23×C67C22×D4
prime radicalC22×C22⋊D67D4
hypercenterC22×#106D67
hypocenterC67C2×#3344
LCSG ▷ C2×C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#106

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
3. #22572660C2direct (N × H)
4. C2×#16863803C2semidirect
5. C2×#16863731C2semidirect
6. C2×#16863740C2semidirect
7. C2×#16863728C2semidirect
8. C2×#16863726C2semidirect
9. C2×#16863706C2semidirect
10. C2×#16863680C2semidirect
11. C2×#16863655C2semidirect
12. C2×#16863637C2semidirect
13. C2×#16863502C2semidirect
15. C2×#16863435C2semidirect
16. C22×#106×C67C2semidirect
42. #16863803C22semidirect
43. #16863740C22semidirect
44. #16863731C22semidirect
45. #16863728C22semidirect
46. #16863726C22semidirect
47. #16863706C22semidirect
48. #16863680C22semidirect
49. #16863655C22semidirect
50. #16863637C22semidirect
51. #16863502C22semidirect
53. #16863435C22semidirect
76. C2×#106×C67C22semidirect
355. C2×C67#3344semidirect
375. C22×#106D67semidirect
376. C67C2×#3344semidirect
426. C2×#106C2×D67semidirect
715. C2#22572660direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#168641012
C2×#168640812
#225726602
C2×#168638032
C2×#168637312
C2×#168637402
C2×#168637282
C2×#168637262
C2×#168637062
C2×#168636802
C2×#168636552
C2×#168636372
C2×#168635022
C2×#168634672
C2×#168634352
C22×#106×C672
C2×#334467